Consider the exponential function . Which of the following best describes the the graph of g?
a. Concave up and increasing
b. Concave up and decreasing
c. Concave down and increasing
d. Concave down and decreasing
The rules are +constant, concave up, - constant concave down.
Base greater than 1 increasing, base less than 1, decreasing.
If you're referring to the problem from the previous exercise, then the constant term is 6.05 and the base is 0.83
c. Concave down and increasing
To determine the behavior of the graph of the exponential function g, we look at the base of the function.
Given that the base of the exponential function is 0.83 (which is less than 1), we know that the function will be decreasing.
Next, let's look at the constant term of 6.05. Since the constant term is positive, we know that the graph will be concave up.
Combining these two findings, we can conclude that the graph of g is concave up and decreasing. Therefore, the best description for the graph of g is option b. Concave up and decreasing.
To determine the best description for the graph of the exponential function g, we need to analyze the properties of the function based on its base and constant term.
First, let's consider the base of the exponential function. In this case, the base is 0.83. The general rule is that if the base is greater than 1, the function increases as x increases; if the base is between 0 and 1, the function decreases as x increases.
Here, since the base (0.83) is between 0 and 1, we can conclude that the function is decreasing.
Next, let's look at the constant term of the exponential function, which is 6.05. The rule is that if the constant term is positive (+), the function is concave up, and if the constant term is negative (-), the function is concave down.
In this case, since the constant term (6.05) is positive (+), we can conclude that the function is concave up.
Combining these conclusions, we can determine that the best description for the graph of g is "Concave up and decreasing" - option b.
Remember to always analyze the base and constant term of the exponential function to determine its behavior: base greater than 1 increases, base between 0 and 1 decreases, constant term positive (+) concave up, and constant term negative (-) concave down.